There is no difference between Contingent Liability and Off Balance Sheet Liability.

Contingent liabilities are not added to total liabilities but shown as a note to financial statements that these are the liabilities that are contingent on certain event

A contingent liability is a potential obligation that may arise in the future, depending on the outcome of a future event. It is documented in the financial statements as a disclosure rather than a recognition in the balance sheet. Contingent liabilities can include pending lawsuits, warranties, or product recalls, and their potential impact on the company's financial position should be clearly outlined in the journal entry.

Contingent liability can impact earnings because it is a projected and future liability. Not knowing what the outcome of the liability is, it can unexpectedly affect a large amount of earnings.